{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ADKY4re5Kx-5"
      },
      "source": [
        "##### Copyright 2018 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "form",
        "colab": {},
        "colab_type": "code",
        "id": "S2AOrHzjK0_L"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "56dF5DnkKx0a"
      },
      "source": [
        "# Gaussian Process Regression in TensorFlow Probability\n",
        "\n",
        "\u003ctable class=\"tfo-notebook-buttons\" align=\"left\"\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/Gaussian_Process_Regression_In_TFP\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" /\u003eView on TensorFlow.org\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Gaussian_Process_Regression_In_TFP.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" /\u003eRun in Google Colab\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Gaussian_Process_Regression_In_TFP.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" /\u003eView source on GitHub\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/Gaussian_Process_Regression_In_TFP.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/download_logo_32px.png\" /\u003eDownload notebook\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "\u003c/table\u003e"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "rTFa-AE9KxFC"
      },
      "source": [
        "In this colab, we explore Gaussian process regression using\n",
        "TensorFlow and TensorFlow Probability. We generate some noisy observations from\n",
        "some known functions and fit GP models to those data. We then sample from the GP\n",
        "posterior and plot the sampled function values over grids in their domains.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "n4-qQf7qZLVI"
      },
      "source": [
        "## Background\n",
        "Let $\\mathcal{X}$ be any set. A *Gaussian process*\n",
        "(GP) is a collection of random variables indexed by $\\mathcal{X}$ such that if\n",
        "$\\{X_1, \\ldots, X_n\\} \\subset \\mathcal{X}$ is any finite subset, the marginal density\n",
        "$p(X_1 = x_1, \\ldots, X_n = x_n)$ is multivariate Gaussian. Any Gaussian\n",
        "distribution is completely specified by its first and second central moments\n",
        "(mean and covariance), and GP's are no exception. We can specify a GP completely\n",
        "in terms of its mean function $\\mu : \\mathcal{X} \\to \\mathbb{R}$ and covariance function\n",
        "$k : \\mathcal{X} \\times \\mathcal{X} \\to \\mathbb{R}$. Most of the expressive power of GP's is encapsulated\n",
        "in the choice of covariance function. For various reasons, the covariance\n",
        "function is also referred to as a *kernel function*. It is required only to be\n",
        "symmetric and positive-definite (see [Ch. 4 of Rasmussen & Williams](\n",
        "http://www.gaussianprocess.org/gpml/chapters/RW4.pdf)). Below we make use of the\n",
        "ExponentiatedQuadratic covariance kernel. Its form is\n",
        "\n",
        "$$\n",
        "k(x, x') := \\sigma^2 \\exp \\left( \\frac{\\|x - x'\\|^2}{\\lambda^2} \\right)\n",
        "$$\n",
        "\n",
        "where $\\sigma^2$ is called the 'amplitude' and $\\lambda$ the *length scale*.\n",
        "The kernel parameters can be selected via a maximum likelihood optimization\n",
        "procedure.\n",
        "\n",
        "A full sample from a GP comprises a real-valued function over the entire space\n",
        "$\\mathcal{X}$ and is in practice impractical to realize; often one chooses a set of\n",
        "points at which to observe a sample and draws function values at these points.\n",
        "This is achieved by sampling from an appropriate (finite-dimensional)\n",
        "multi-variate Gaussian.\n",
        "\n",
        "Note that, according to the above definition, any finite-dimensional\n",
        "multivariate Gaussian distribution is also a Gaussian process. Usually, when\n",
        "one refers to a GP, it is implicit that the index set is some $\\mathbb{R}^n$\n",
        "and we will indeed make this assumption here.\n",
        "\n",
        "A common application of Gaussian processes in machine learning is Gaussian\n",
        "process regression. The idea is that we wish to estimate an unknown function\n",
        "given noisy observations $\\{y_1, \\ldots, y_N\\}$ of the function at a finite\n",
        "number of points $\\{x_1, \\ldots x_N\\}.$ We imagine a generative process\n",
        "\n",
        "$$\n",
        "\\begin{align}\n",
        "f \\sim \\: & \\textsf{GaussianProcess}\\left(\n",
        "    \\text{mean_fn}=\\mu(x),\n",
        "    \\text{covariance_fn}=k(x, x')\\right) \\\\\n",
        "y_i \\sim \\: & \\textsf{Normal}\\left(\n",
        "    \\text{loc}=f(x_i),\n",
        "    \\text{scale}=\\sigma\\right), i = 1, \\ldots, N\n",
        "\\end{align}\n",
        "$$\n",
        "\n",
        "As noted above, the sampled function is impossible to compute, since we would\n",
        "require its value at an infinite number of points. Instead, one considers a\n",
        "finite sample from a multivariate Gaussian.\n",
        "\n",
        "$$\n",
        "  \\begin{gather}\n",
        "    \\begin{bmatrix}\n",
        "      f(x_1) \\\\\n",
        "      \\vdots \\\\\n",
        "      f(x_N)\n",
        "    \\end{bmatrix}\n",
        "    \\sim\n",
        "    \\textsf{MultivariateNormal} \\left( \\:\n",
        "      \\text{loc}=\n",
        "      \\begin{bmatrix}\n",
        "        \\mu(x_1) \\\\\n",
        "        \\vdots \\\\\n",
        "        \\mu(x_N)\n",
        "      \\end{bmatrix} \\:,\\:\n",
        "      \\text{scale}=\n",
        "      \\begin{bmatrix}\n",
        "        k(x_1, x_1) & \\cdots & k(x_1, x_N) \\\\\n",
        "        \\vdots & \\ddots & \\vdots \\\\\n",
        "        k(x_N, x_1) & \\cdots & k(x_N, x_N) \\\\\n",
        "      \\end{bmatrix}^{1/2}\n",
        "    \\: \\right)\n",
        "  \\end{gather} \\\\\n",
        "  y_i \\sim \\textsf{Normal} \\left(\n",
        "      \\text{loc}=f(x_i),\n",
        "      \\text{scale}=\\sigma\n",
        "  \\right)\n",
        "$$\n",
        "\n",
        "Note the exponent $\\frac{1}{2}$ on the covariance matrix: this denotes a\n",
        "Cholesky decomposition. Comptuing the Cholesky is necessary because the MVN is\n",
        "a location-scale family distribution. Unfortunately the Cholesky decomposition\n",
        "is computationally expensive, taking $O(N^3)$ time and $O(N^2)$ space. Much of\n",
        "the GP literature is focused on dealing with this seemingly innocuous little\n",
        "exponent.\n",
        "\n",
        "It is common to take the prior mean function to be constant, often zero. Also,\n",
        "some notational conventions are convenient. One often writes $\\mathbf{f}$ for the\n",
        "finite vector of sampled function values. A number of interesting notations are\n",
        "used for the covariance matrix resulting from the application of $k$ to pairs of\n",
        "inputs. Following [(Quiñonero-Candela, 2005)][QuinoneroCandela2005], we note\n",
        "that the components of the matrix are covariances of function values at\n",
        "particular input points. Thus we can denote the covariance matrix as $K_{AB}$\n",
        "where $A$ and $B$ are some indicators of the collection of function values along\n",
        "the given matrix dimensions.\n",
        "\n",
        "[QuinoneroCandela2005]: http://www.jmlr.org/papers/volume6/quinonero-candela05a/quinonero-candela05a.pdf\n",
        "\n",
        "For example, given observed data $(\\mathbf{x}, \\mathbf{y})$ with implied latent function\n",
        "values $\\mathbf{f}$, we can write\n",
        "\n",
        "$$\n",
        "K_{\\mathbf{f},\\mathbf{f}} = \\begin{bmatrix}\n",
        "  k(x_1, x_1) & \\cdots & k(x_1, x_N) \\\\\n",
        "  \\vdots & \\ddots & \\vdots \\\\\n",
        "  k(x_N, x_1) & \\cdots & k(x_N, x_N) \\\\\n",
        "\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "Similarly, we can mix sets of inputs, as in\n",
        "\n",
        "$$\n",
        "K_{\\mathbf{f},*} = \\begin{bmatrix}\n",
        "  k(x_1, x^*_1) & \\cdots & k(x_1, x^*_T) \\\\\n",
        "  \\vdots & \\ddots & \\vdots \\\\\n",
        "  k(x_N, x^*_1) & \\cdots & k(x_N, x^*_T) \\\\\n",
        "\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "where we suppose there are $N$ training inputs, and $T$ test inputs. The above\n",
        "generative process may then be written compactly as\n",
        "\n",
        "$$\n",
        "\\begin{align}\n",
        "\\mathbf{f} \\sim \\: & \\textsf{MultivariateNormal} \\left(\n",
        "        \\text{loc}=\\mathbf{0},\n",
        "        \\text{scale}=K_{\\mathbf{f},\\mathbf{f}}^{1/2}\n",
        "    \\right) \\\\\n",
        "y_i \\sim \\: & \\textsf{Normal} \\left(\n",
        "    \\text{loc}=f_i,\n",
        "    \\text{scale}=\\sigma \\right), i = 1, \\ldots, N\n",
        "\\end{align}\n",
        "$$\n",
        "\n",
        "The sampling operation in the first line yields a finite set of $N$ function\n",
        "values from a multivariate Gaussian -- *not an entire function as in the above\n",
        "GP draw notation*. The second line describes a collection of $N$ draws from\n",
        "*univariate* Gaussians centered at the various function values, with fixed\n",
        "observation noise $\\sigma^2$.\n",
        "\n",
        "With the above generative model in place, we can proceed to consider the\n",
        "posterior inference problem. This yields a posterior distribution over function\n",
        "values at a new set of test points, conditioned on the observed noisy data from\n",
        "the process above.\n",
        "\n",
        "With the above notation in place, we can compactly write the posterior\n",
        "predictive distribution over future (noisy) observations conditional on\n",
        "corresponding inputs and training data as follows (for more details, see §2.2 of\n",
        "[Rasmussen & Williams](http://www.gaussianprocess.org/gpml/)). \n",
        "\n",
        "$$\n",
        "\\mathbf{y}^* \\mid \\mathbf{x}^*, \\mathbf{x}, \\mathbf{y} \\sim \\textsf{Normal} \\left(\n",
        "    \\text{loc}=\\mathbf{\\mu}^*,\n",
        "    \\text{scale}=(\\Sigma^*)^{1/2}\n",
        "\\right),\n",
        "$$\n",
        "\n",
        "where\n",
        "\n",
        "$$\n",
        "\\mathbf{\\mu}^* = K_{*,\\mathbf{f}}\\left(K_{\\mathbf{f},\\mathbf{f}} + \\sigma^2 I \\right)^{-1} \\mathbf{y}\n",
        "$$\n",
        "\n",
        "and\n",
        "\n",
        "$$\n",
        "\\Sigma^* = K_{*,*} - K_{*,\\mathbf{f}}\n",
        "    \\left(K_{\\mathbf{f},\\mathbf{f}} + \\sigma^2 I \\right)^{-1} K_{\\mathbf{f},*}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "QF_BW8m_c3_d"
      },
      "source": [
        "## Imports"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "code",
        "colab": {
          "height": 34
        },
        "colab_type": "code",
        "id": "jw-_1yC50xaM",
        "outputId": "1de9e862-2aef-400d-be50-d14888c177a9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ]
        }
      ],
      "source": [
        "import time\n",
        "\n",
        "import numpy as np\n",
        "import tensorflow.compat.v2 as tf\n",
        "import tensorflow_probability as tfp\n",
        "tfb = tfp.bijectors\n",
        "tfd = tfp.distributions\n",
        "tfk = tfp.math.psd_kernels\n",
        "tf.enable_v2_behavior()\n",
        "\n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "%pylab inline\n",
        "# Configure plot defaults\n",
        "plt.rcParams['axes.facecolor'] = 'white'\n",
        "plt.rcParams['grid.color'] = '#666666'\n",
        "%config InlineBackend.figure_format = 'png'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "cu9S6c7uuvC1"
      },
      "source": [
        "## Example: Exact GP Regression on Noisy Sinusoidal Data\n",
        "Here we generate training data from a noisy sinusoid, then sample a bunch of\n",
        "curves from the posterior of the GP regression model. We use\n",
        "[Adam](https://arxiv.org/abs/1412.6980) to optimize the kernel hyperparameters\n",
        "(we minimize the negative log likelihood of the data under the prior). We\n",
        "plot the training curve, followed by the true function and the posterior\n",
        "samples."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "Qrys68xzZE-c"
      },
      "outputs": [],
      "source": [
        "def sinusoid(x):\n",
        "  return np.sin(3 * np.pi * x[..., 0])\n",
        "\n",
        "def generate_1d_data(num_training_points, observation_noise_variance):\n",
        "  \"\"\"Generate noisy sinusoidal observations at a random set of points.\n",
        "\n",
        "  Returns:\n",
        "     observation_index_points, observations\n",
        "  \"\"\"\n",
        "  index_points_ = np.random.uniform(-1., 1., (num_training_points, 1))\n",
        "  index_points_ = index_points_.astype(np.float64)\n",
        "  # y = f(x) + noise\n",
        "  observations_ = (sinusoid(index_points_) +\n",
        "                   np.random.normal(loc=0,\n",
        "                                    scale=np.sqrt(observation_noise_variance),\n",
        "                                    size=(num_training_points)))\n",
        "  return index_points_, observations_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "Tem9p8rUlqQR"
      },
      "outputs": [],
      "source": [
        "# Generate training data with a known noise level (we'll later try to recover\n",
        "# this value from the data).\n",
        "NUM_TRAINING_POINTS = 100\n",
        "observation_index_points_, observations_ = generate_1d_data(\n",
        "    num_training_points=NUM_TRAINING_POINTS,\n",
        "    observation_noise_variance=.1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "JiJukqfWuXUq"
      },
      "source": [
        "We'll put priors on the kernel hyperparameters, and write the joint distribution of the hyperparameters and observed data using `tfd.JointDistributionNamed`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "i63dMy4FbnTd"
      },
      "outputs": [],
      "source": [
        "def build_gp(amplitude, length_scale, observation_noise_variance):\n",
        "  \"\"\"Defines the conditional dist. of GP outputs, given kernel parameters.\"\"\"\n",
        "\n",
        "  # Create the covariance kernel, which will be shared between the prior (which we\n",
        "  # use for maximum likelihood training) and the posterior (which we use for\n",
        "  # posterior predictive sampling)\n",
        "  kernel = tfk.ExponentiatedQuadratic(amplitude, length_scale)\n",
        "\n",
        "  # Create the GP prior distribution, which we will use to train the model\n",
        "  # parameters.\n",
        "  return tfd.GaussianProcess(\n",
        "      kernel=kernel,\n",
        "      index_points=observation_index_points_,\n",
        "      observation_noise_variance=observation_noise_variance)\n",
        "\n",
        "gp_joint_model = tfd.JointDistributionNamed({\n",
        "    'amplitude': tfd.LogNormal(loc=0., scale=np.float64(1.)),\n",
        "    'length_scale': tfd.LogNormal(loc=0., scale=np.float64(1.)),\n",
        "    'observation_noise_variance': tfd.LogNormal(loc=0., scale=np.float64(1.)),\n",
        "    'observations': build_gp,\n",
        "})"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "sNprcU_0umhK"
      },
      "source": [
        "We can sanity-check our implementation by verifying that we can sample from the prior, and compute the log-density of a sample."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 411
        },
        "colab_type": "code",
        "id": "HK1Pyen7ci_A",
        "outputId": "81385927-9b77-4520-f264-3eff5b8964b2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "sampled {'length_scale': \u003ctf.Tensor: shape=(), dtype=float64, numpy=9.526471247059396\u003e, 'observation_noise_variance': \u003ctf.Tensor: shape=(), dtype=float64, numpy=0.7266366332947352\u003e, 'amplitude': \u003ctf.Tensor: shape=(), dtype=float64, numpy=1.6714059577238705\u003e, 'observations': \u003ctf.Tensor: shape=(100,), dtype=float64, numpy=\n",
            "array([3.28671007, 3.68127692, 1.46988415, 1.77062709, 1.67811476,\n",
            "       2.55931267, 1.65328635, 1.73481701, 2.30216517, 1.29280539,\n",
            "       2.48049681, 2.06504851, 1.24508666, 1.76258146, 1.1567751 ,\n",
            "       1.12563896, 0.88050047, 2.62427676, 3.35178458, 0.89685013,\n",
            "       3.22490858, 2.41177716, 2.09414069, 1.77904813, 0.16945602,\n",
            "       2.53614107, 1.81245418, 1.35642751, 3.68498843, 1.82001509,\n",
            "       2.03604088, 3.81705144, 3.18142879, 0.57016071, 1.68918439,\n",
            "       2.85699517, 2.14177352, 3.72928207, 2.17608584, 3.28719282,\n",
            "       0.6005666 , 1.96646054, 2.13131158, 1.95124967, 0.59090051,\n",
            "       3.2427046 , 0.83849964, 1.35907388, 2.86403843, 1.56229808,\n",
            "       1.47042658, 1.67109072, 3.20026542, 3.5325695 , 3.5645868 ,\n",
            "       2.62192175, 2.68818167, 3.11055677, 2.67670315, 1.3779872 ,\n",
            "       1.06653007, 2.15629192, 2.29109232, 2.48774572, 2.49993369,\n",
            "       1.87633097, 4.14883802, 1.28336995, 0.62767486, 2.3908827 ,\n",
            "       2.59999376, 1.84284938, 2.52603837, 1.25639193, 2.48792358,\n",
            "       0.95560965, 2.59174573, 3.06116313, 2.30181874, 1.64854234,\n",
            "       2.20463203, 0.86536671, 1.18708743, 1.88104063, 2.55473466,\n",
            "       1.94555342, 1.64555061, 2.55028422, 0.86947597, 2.3485391 ,\n",
            "       0.92084282, 1.51403219, 2.1829704 , 2.02841574, 1.0644413 ,\n",
            "       3.26609039, 2.32084387, 2.74834809, 2.5470367 , 2.51504817])\u003e}\n",
            "log_prob of sample: -137.270757398\n"
          ]
        }
      ],
      "source": [
        "x = gp_joint_model.sample()\n",
        "lp = gp_joint_model.log_prob(x)\n",
        "\n",
        "print(\"sampled {}\".format(x))\n",
        "print(\"log_prob of sample: {}\".format(lp))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Cw50WxSmu3Ge"
      },
      "source": [
        "Now let's optimize to find the parameter values with highest posterior probability. We'll define a variable for each parameter, and constrain their values to be positive."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "ByXndE3pkA4x"
      },
      "outputs": [],
      "source": [
        "# Create the trainable model parameters, which we'll subsequently optimize.\n",
        "# Note that we constrain them to be strictly positive.\n",
        "\n",
        "constrain_positive = tfb.Shift(np.finfo(np.float64).tiny)(tfb.Exp())\n",
        "\n",
        "amplitude_var = tfp.util.TransformedVariable(\n",
        "    initial_value=1.,\n",
        "    bijector=constrain_positive,\n",
        "    name='amplitude',\n",
        "    dtype=np.float64)\n",
        "\n",
        "length_scale_var = tfp.util.TransformedVariable(\n",
        "    initial_value=1.,\n",
        "    bijector=constrain_positive,\n",
        "    name='length_scale',\n",
        "    dtype=np.float64)\n",
        "\n",
        "observation_noise_variance_var = tfp.util.TransformedVariable(\n",
        "    initial_value=1.,\n",
        "    bijector=constrain_positive,\n",
        "    name='observation_noise_variance_var',\n",
        "    dtype=np.float64)\n",
        "\n",
        "trainable_variables = [v.trainable_variables[0] for v in \n",
        "                       [amplitude_var,\n",
        "                       length_scale_var,\n",
        "                       observation_noise_variance_var]]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "2Ji95UUYvE-K"
      },
      "source": [
        "To condition the model on our observed data, we'll define a `target_log_prob` function, which takes the (still to be inferred) kernel hyperparameters."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "yjO8TWIXvFr5"
      },
      "outputs": [],
      "source": [
        "# Use `tf.function` to trace the loss for more efficient evaluation.\n",
        "@tf.function(autograph=False, experimental_compile=False)\n",
        "def target_log_prob(amplitude, length_scale, observation_noise_variance):\n",
        "  return gp_joint_model.log_prob({\n",
        "      'amplitude': amplitude,\n",
        "      'length_scale': length_scale,\n",
        "      'observation_noise_variance': observation_noise_variance,\n",
        "      'observations': observations_\n",
        "  })"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 85
        },
        "colab_type": "code",
        "id": "4swUVjI0DZY4",
        "outputId": "ae9fd757-d52d-48b1-ba68-97f8ca023164"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Trained parameters:\n",
            "amplitude: 0.875065718641\n",
            "length_scale: 0.176252877463\n",
            "observation_noise_variance: 0.0971537576792\n"
          ]
        }
      ],
      "source": [
        "# Now we optimize the model parameters.\n",
        "num_iters = 1000\n",
        "optimizer = tf.optimizers.Adam(learning_rate=.01)\n",
        "\n",
        "# Store the likelihood values during training, so we can plot the progress\n",
        "lls_ = np.zeros(num_iters, np.float64)\n",
        "for i in range(num_iters):\n",
        "  with tf.GradientTape() as tape:\n",
        "    loss = -target_log_prob(amplitude_var, length_scale_var,\n",
        "                            observation_noise_variance_var)\n",
        "  grads = tape.gradient(loss, trainable_variables)\n",
        "  optimizer.apply_gradients(zip(grads, trainable_variables))\n",
        "  lls_[i] = loss\n",
        "\n",
        "print('Trained parameters:')\n",
        "print('amplitude: {}'.format(amplitude_var._value().numpy()))\n",
        "print('length_scale: {}'.format(length_scale_var._value().numpy()))\n",
        "print('observation_noise_variance: {}'.format(observation_noise_variance_var._value().numpy()))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 317
        },
        "colab_type": "code",
        "id": "QKS1ZvcEuHZs",
        "outputId": "c9995531-6783-4892-bb61-9d2bc04bc303"
      },
      "outputs": [
        {
          "data": {
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kE2zduhVxcXFIS0sz+ULp6emIiIhAdXU1pk2bhjFjxtxyHADS0tKwevVqREVFYe3atXjl\nlVfu7Ltr5Xp17QAA+OXQKYmTEBEREZElmDSzvn//fnz00UcGSy2mTp2KFStWmHyhhQsXYuHChSaP\nA0BQUBDy8/NNvkZb4+3hCIWnI/b8dhqxQyzzDgcRERERScekmXVvb2+UlpYajP3444/w9va2SCgy\n3b3BXth3pOamrS+JiIiIqOUzaWZ93rx5ePbZZ/HQQw/Bz88PJ0+eRElJCd544w1L56PbuKeTBzaX\nVuDk6Xr4d2gvdRwiIiIiMiOTZtaHDRuGgoICdOvWDfX19ejWrRsKCgpu+lRTan4hna7dcHvg91qJ\nkxARERGRuZm8dWOXLl3wzDPP4PTp0/Dy8oJMZlKfTxYW4OOMdvY22P97HSL78cORiIiIiFoTkzru\n8+fP44UXXkCvXr0QERGBXr16YcGCBTh37pyl89FtyGUCugW64WBFndRRiIiIiMjMTGrW09PTcfHi\nRSiVSvzyyy9QKpW4ePEi0tPTLZ2PTHBPJ3ccPanBpStXpY5CRERERGZk0jKYbdu24auvvkK7du0A\nXFsS89prr2HEiBEWDUemuaejO3Q6EUcqzyK0i6fUcYiIiIjITEyaWbe3t0dtreENjHV1dbCzs7NI\nKLozQf5uAICjlWclTkJERERE5mTSzPqECRPw5JNPYtq0afqtGz/++GM89thjls5HJvByc4Czox2O\nnNRIHYWIiIiIzMikZn3mzJnw9vZGYWEhqqur4e3tjenTp2PChAmWzkcmEAQBQf4uOHKSM+tERERE\nrYlJzbogCJgwYQKbcyvWxc8VX+w4iqtaHWzk3FaTiIiIqDUweZ/17du3o7y8HBcuXDAYnzNnjtlD\n0Z0L9ndFw1UdKqvPo5Ovi9RxiIiIiMgMTGrWFy1ahP/9738IDw/X7whD1qWLvysA4MjJs2zWiYiI\niFoJk5r1L774AuvXr4evr6+l81ATBXRoD1sbGY5UnsXQvoFSxyEiIiIiMzBpcbObmxucnZ0tnYXu\nglwuQ6C3Myqq+KmyRERERK1FozPrx48f1z9+4oknMH/+fCQkJMDLy8vgeYGBnMW1FoE+zig7ViN1\nDCIiIiIyk0ab9REjRkAQBIiiqB8rKSkxeI4gCCgvLzfpQpmZmdi0aRMqKytRWFiIrl27AgCOHTuG\npKQknDlzBm5ubliyZAk6dux422N0s44KZ3zz8wlcuNQARwdbqeMQERER0V1qtFnfv3+/WS80YsQI\nTJs2DZMmTTIYT01NRXx8PGJiYrBx40akpKQgLy/vtsfoZh0V15YqHa86h3s6eUichoiIiIjuVrNt\nyB0WFgYfHx+Dmfra2lqUl5cjOjoaABATE4OysjLU1dXd8hgZ19Hnr2adiIiIiFq+RmfWn3rqKXzw\nwQcAgEmTJkEQBKPPW7NmTZMvrlKp4OPjoz+3TCaDt7c31Go1dDpdo8fc3d1vOpdGo4FGozEYk8vl\nbWoHGx9PJ9jZyPC7ms06ERERkRRUKhW0Wq3BmIuLC1xcmra1dqPN+rhx4/SPH3300SadvDnl5eUh\nOzvbYMzf3x/FxcVITk5GTU3buPFS1+4B/G+LGqVfZEkdxeolJCRIHYGsEOuCjGFdkDGsC7qep6cn\nMjIyMHnyZFRWVhocS0xMxKxZs5p03kab9TFjxugfjx8/vkknvx1fX19UVVVBFEUIggCdTofq6moo\nFAqIotjoMWOmTp16U065XA4AyMjIsEh+a/Tm6p9QdqwGuQufljqKVUtISEBubq7UMcjKsC7IGNYF\nGcO6oMasWbPG6Mx6UzXarH/22WcmnWDChAl3fNE/1617eHggJCQESqUSsbGxUCqVCA0N1S9zudWx\nG93N2wutCXeEISIiIpKOuZdgN9qsb9iw4bYvFgTB5GY9PT0dmzdvRk1NDZ544gm4u7tDqVQiLS0N\nSUlJyMnJgaurKzIzM/WvudUxMo47whARERG1Ho026//617/MeqGFCxdi4cKFN40HBQUhPz/f6Gtu\ndYyMu35HGDbrRERERC2byVs31tXVYf369Vi1ahUAoKqqCmq12mLBqGm4IwwRERFR62FSs15aWoqo\nqCgolUq8++67AIDff/8daWlplsxGTSCXCfD3bo8T1eeljkJEREREd8mkZj0jIwPLli3DBx98ABub\naytnevfujT179lg0HDVNoLczKvjBSEREREQtnknNemVlJQYNGgQA+g8psrW1vWlbGrIOgQpnnKq7\ngEuXr0odhYiIiIjugknNenBwMLZt22Yw9u2336J79+4WCUV3J9DbGaIInDjFpTBERERELVmju8Fc\nLykpCQkJCXjooYdw6dIlvPzyyyguLkZOTo6l81ETBPi0BwCcqDqHrgFuEqchIiIioqYyaWa9T58+\n2LhxI7p27YpHHnkEAQEB+Oyzz9CrVy9L56Mm8PNqD5lMwHHeZEpERETUopk0s37o0CF07doVTz9t\n+BH227Ztw5AhQywSjJrO1kYGX08nHOdNpkREREQtmkkz6wkJCTh+/LjBWHFxMV588UWLhKK711Hh\nzGadiIiIqIUzqVl/4YUXMH36dFRXVwMANm3ahJdffhkrVqywaDhqugDv9jh5uh4NV3VSRyEiIiKi\nJjJpGcyoUaNw/vx5PPnkk5g0aRJycnKwatUqhISEWDofNVGgjzN0OhGq0+fRUeEidRwiIiIiaoJG\nm3WdznBGdvz48Th79ixycnLwwQcfoFu3btDpdJDJTJqcp2YW6OMMADhezWadiIiIqKVqtFkPDQ3V\nfwDSn0RRBACMGzcOoihCEASUl5dbNiE1SUCHa9s3ct06ERERUcvVaLO+ZcuW5sxBZuZgbwNvD0c2\n60REREQtWKPNur+/f3PmIAsI9G7PZp2IiIioBWu0WU9JScHixYsBAP/85z9vWhLzpyVLlpglSElJ\nCd555x1cvXoVrq6ueP311+Hv749jx44hKSkJZ86cgZubG5YsWYKOHTua5ZqtXaCPM/YeOg2tToRc\nZvzvj4iIiIisV6PNekBAgP5xp06dLBpCo9EgKSkJ+fn56NixIzZu3IjU1FSsWrUKqampiI+PR0xM\nDDZu3IiUlBTk5eVZNE9rEejjjCtXdThVdwEKTyep4xARERHRHWq0WU9ISNA/TkxMtGiI33//HR06\ndNDPmEdERGDBggWora1FWVkZoqOjAQAxMTFYvHgx6urq4O7ubtFMrUGg97UdYSqqzrFZJyIiImqB\nGm3Wv/vuO5NOMGjQoLsO0aVLF5w6dQq//vorevbsiY0bNwIAVCoVFAqFfgmOTCaDt7c31Go1m3UT\nBPpc2xHmRNU5DAhVSJyGiIiIiO5Uo836Sy+9dNsXC4Jgll1j2rdvj6VLlyIjIwNXrlzBgw8+CBcX\nF1y4cEG/XeTtaDQaaDQagzG5XA5fX9+7ztdStXe0g7uzPY5XnZc6ChEREVGboFKpoNVqDcZcXFzg\n4tK0z70RRFO74WZUU1ODyMhIFBUVITY2FqWlpRAEATqdDuHh4di0adNNM+tZWVnIzs42GPP390dx\ncTGSk5NRU1PTnN+C1TjtMACiIEeHi6a9U0JEREREd87T0xMZGRmIjIxEZWWlwbHExETMmjWrSee1\nmmb99OnT8PLygk6nQ0pKCpydnZGUlIQpU6ZgwoQJiI2NxYYNG1BQUGD0BlPOrBuXW7AHW36swL/T\noyHjjjB6CQkJyM3NlToGWRnWBRnDuiBjWBfUGHPPrDe6DKa5LVu2DLt27cLVq1fxwAMP4LnnngMA\npKWlISkpCTk5OXB1dUVmZqbR19/NH0Jr1sXfFRd3aFFVewG+XrzJlIiIiMiSzD1RbDXNenp6utHx\noKAg5OfnN3Oa1iPIzxUAcKTyLJt1IiIiohZGJnUAsqyOCmfIZAKOnDwrdRQiIiIiukONzqzrdDqT\nTiCTsd+3Zna2cgR6t8eRSjbrRERERC1No816aGiofn9zY0RRhCAIKC8vt0gwMp8u/q7Ye+i01DGI\niIiI6A412qybY/90sg5Bfq4o+ekEzp6/DNf29lLHISIiIiITNdqs+/v7N2cOsqAg/2s3mR46cQZ9\nQ3wkTkNEREREpjJ5N5gtW7bghx9+QF1dncGnii5ZssQiwch8ugW6QRCAA7/XsVknIiIiakFMujs0\nOzsbqamp0Ol0KCoqgpubG7Zv3859zVsIRwdbdFK4YP+xWqmjEBEREdEdMKlZ//zzz/Hhhx8iOTkZ\ntra2SE5OxooVK3DixAlL5yMzuaeTOw5W1EGns4oPrCUiIiIiE5jUrGs0GnTv3h0AYGtri4aGBvTq\n1Qs//PCDRcOR+YR08kD9pas4UX1O6ihEREREZCKT1qx37NgRv/32G7p164Zu3bph3bp1cHFxgaur\nq6XzkZmEdHYHAOz/vQ4dFVy+RERERNQSmNSsz507F2fOnAEAPP/885g/fz4uXLiA1NRUi4Yj8/Hv\n0B7OjnbYd6QGI8M7SR2HiIiIiExgUrMeERGhf9y7d29s3rzZYoHIMgRBQK+uXtjz2yn9B1oRERER\nkXUzeevGc+fO4ejRo6ivrzcYHzRokNlDkWX06d4BO/acxInq8wj0cZY6DhERERHdhknNekFBARYt\nWgRHR0c4ODjoxwVB4CedtiB9uncAAOw+eIrNOhEREVELYFKzvnTpUixfvtxgOQy1PApPJ/h6OmH3\nwVMYMyRI6jhEREREdBsmbd2o1WoxePBgS2ehZtCnewfsOXQKVxq0UkchIiIiotswqVl/+umn8d57\n70Gn01ksyNdff43x48dj3LhxGDt2rP4m1mPHjiEuLg5RUVGIi4tDRUWFxTK0BQN7+uLSFS12Hzwl\ndRQiIiIiug2TlsF8/PHHOH36NFatWgU3NzeDYyUlJWYJsmDBAqxbtw7BwcE4cOAAJk6ciBEjRiA1\nNRXx8fGIiYnBxo0bkZKSgry8PLNcsy26t6sXnNrZYseekxjwN4XUcYiIiIjoFkxq1t944w1L54BM\nJoNGowFw7RNTvb29UVtbi7KyMkRHRwMAYmJisHjxYtTV1cHd3d3imVojWxsZwv+mQOk+Na5qdbCR\nm/TmChERERFJwKRmfcCAAZbOgaVLl2LmzJlwdHREfX09Vq5cCZVKBYVCod8TXCaTwdvbG2q1ms36\nXbj/Xl8U/3gcuw+eQr8ePlLHISIiIqJGNNqsv/fee5g5cyYAYPny5Y2eYM6cOXcdQqvVYuXKlVix\nYgX69OmDXbt2Ye7cuViyZInJ59BoNPqZ+T/J5XL4+vredb7WJizEB86Odvjqhwo260RERERmpFKp\noNUabuTh4uICFxeXJp2v0WZdrVYbfWwJ5eXlOHXqFPr06QMACAsLQ7t27WBvb4+qqir9J27qdDpU\nV1dDobh5rXVeXh6ys7MNxvz9/VFcXIzk5GTU1NRY9HtoaXR2PbBj90U8vSMPMjRIHUcSCQkJUkcg\nK8S6IGNYF2QM64Ku5+npiYyMDEyePBmVlZUGxxITEzFr1qwmnVcQRVE0R8C7cfr0aURFReHTTz9F\nly5dcPjwYUyaNAmbN29GYmIiJkyYgNjYWGzYsAEFBQVGbzDlzPqdOVJ5FnPeLkHC+HsRM7jt7bme\nkJCA3NxcqWOQlWFdkDGsCzKGdUGNabaZ9esdP37c6LidnR06dOgAmezublL08vJCWloaZs+eDblc\nDgB47bXX4OLigrS0NCQlJSEnJweurq7IzMw0eo67+UNoi4L8XdE1wBX//fYooh/oor8vgIiIiIia\nztwTxSY16yNGjNA3c38uSfmTTCZDZGQkUlNT4eXl1eQgMTExiImJuWk8KCgI+fn5TT4vNW7MkGAs\nXbcLPx88hbB7vKWOQ0REREQ3MGlKfPHixRgzZgy+/PJL7NmzB0VFRYiNjUVqaio2btyIq1evYtGi\nRZbOSmY2pI8f3JztsXHrYamjEBEREZERJs2sZ2VlYfPmzbC3twcAdOrUCWlpaRg1ahS2bt2K119/\nHSNHjrRoUDI/Wxs5Rt/fBWu/3I8T1ecQ4O0sdSQiIiIiuo5JM+s6nQ4nTpwwGDt58iR0Oh0AwNHR\n8aaF9NQyRA3qBBu5DBu2HpE6ChERERHdwKSZ9alTp2Lq1Kl45JFHoFAooFarUVBQgClTpgAAvvnm\nG/22i9S2mLuxAAAgAElEQVSyuDs7YFj/QHxVWoG4Ed3h6dpO6khERERE9AeTmvWnn34a99xzD4qK\nirBv3z506NABr776Kh588EEAwPDhwzF8+HCLBiXLmRDZDZtLK1BQcghPj71X6jhERERE9IfbNuta\nrRbJyclYvHixvjmn1kXh6YSHwgJQ9N3veDSyO9yc7aWOREREREQwYc26XC7Hjh07uA93K/fosG5o\nuKrF+m8OSR2FiIiIiP5g0g2mU6dORVZWFhoa2ubH0rcFAd7OGNLbH//99ijOXbgidRwiIiIigolr\n1levXo3Tp0/jo48+goeHh8Ese0lJiaWyUTN7dHh3bN1dCeW2I5g0KkTqOERERERtnknN+htvvGHp\nHGQFOvu6YNC9vti49TBiHwxG+3a2UkciIiIiatNMatYHDBhg6RxkJSaOvAff7VVh/TeHEB/VQ+o4\nRERERG2aSc06AJSXl+PHH39EXV0dRFHUj8+ZM8ciwUgaXfxc8UBvP2zcehhjBgfBtT13hiEiIiKS\nikk3mH7yySeYOHEivv/+e7z//vs4ePAgPvroI1RUVFg6H0lg8qgQXL6iRcHX3BmGiIiISEomNeur\nVq3CqlWr8O6778LBwQHvvvsuli9fDhsbkyfmqQUJ9HFGRFgACnccRa3mktRxiIiIiNosk5r1mpoa\n9OvX79oLZDLodDpERETg66+/tmg4ks7EkSG4qtXh0y0HpY5CRERE1GaZ1KwrFAqcOHECANC5c2ds\n2bIFP/74I2xtuVtIa+Xr5YQRAzqi6LvfUV13Qeo4RERERG2SSetYpk+fjsOHDyMgIADPPvss5syZ\ng4aGBrz00ktmCVFZWYl//OMf+v3bz549i/r6euzcuRNHjx7Fiy++iDNnzsDNzQ1LlixBx44dzXJd\nurXHhnfHlh+OI/+rg0h8tI/UcYiIiIjaHJOa9b///e/6xxERESgtLUVDQwOcnJzMEsLf3x/r16/X\nf52RkQGdTgcASEtLQ3x8PGJiYrBx40akpKQgLy/PLNelW/N2d0TUwE7433fH8MjQbvD1Ms/fNxER\nERGZxqRlMH86f/48qqqqUFdXp39sbg0NDVAqlZgwYQJqa2tRXl6O6OhoAEBMTAzKyspQV1dn9uuS\ncY8O7w65TMDaTfuljkJERETU5pg0s/7tt98iJSUFJ0+eNNhjXRAElJeXmzXQli1boFAoEBISgn37\n9sHHx0e/PEYmk8Hb2xtqtRru7u4Gr9NoNNBoNAZjcrkcvr6+Zs3X1ni4OCD2wWB8/vVvGPdgMIID\n3KSORERERGS1VCoVtFqtwZiLiwtcXFyadD5BvL77bsTQoUPx7LPPYvTo0XBwcDA4JpfLm3ThxsyY\nMQMPPvgg4uPjsW/fPiQlJUGpVOqPR0dH480330SPHoafrpmVlYXs7GyDMX9/fxQXFyM5ORk1NTVm\nzdmW6GCDKqeHYKc9C89LP0gdh4iIiMjqeHp6IiMjA5GRkaisrDQ4lpiYiFmzZjXpvCY16/fffz+2\nbdtm9sb8RtXV1Rg1ahRKSkrg6uqK2tpaREVFYefOnRAEATqdDuHh4di0aRNn1pvZhq2HsWrDr3hl\nxiCE3eMtdZy7lpCQgNzcXKljkJVhXZAxrAsyhnVBjTH3zLpJa9anTZuGVatWwYS+/q4UFBTgoYce\ngqurKwDAw8MDISEh+pl1pVKJ0NDQmxp14NofQkBAgMEvNurmM/r+zvDxcMTHhfug01m2DoiIiIha\nKl9f35t60qY26oCJzfrIkSORn5+Pvn37YtiwYQa/zGn9+vWYMGGCwVhaWhpWr16NqKgorF27Fq+8\n8opZr0mmsbWRY8roHjh6UoOSXSekjkNERETUJph0g+ns2bPRr18/REVF3bRm3ZyKiopuGgsKCkJ+\nfr7FrkmmG9zbH//55jBWF5VjcG8/2NladlkUERERUVtnUrN+4sQJrF+/HjLZHe30SK2MTCbgiZhQ\nvPTetyjcfgR/H9pN6khERERErZpJ3fewYcPw/fffWzoLtQC9unZA/1Af/HvzQdRqLkkdh4iIiKhV\nM2lm/cqVK5g5cyb69esHT09Pg2NLliyxSDCyXtPH9sQ/lnyNjwr34flJfaWOQ0RERNRqmdSsd+vW\nDd26cckDXePn1R5/H9oV+V8dRNTAzvhbkOftX0REREREd8ykZj0xMdHSOaiFeTSyG4p/PI4VBXuw\nbF4E5HLez0BERERkbuywqEkc7G0wfWxPHFNpUPTdManjEBEREbVKbNapye6/1xd9unXAv4r282ZT\nIiIiIgtgs05NJggCnnmkF640aLGiYI/UcYiIiIhaHTbrdFf8O7THpFEh+G6vCjv2nJQ6DhEREVGr\nYtINpp999pnRcTs7OygUCvTp0wd2dnZmDUYtx/iIYGz/pRIrCvagV1cvODuyFoiIiIjMwaRmfcOG\nDfj555/h5eUFhUIBtVqN06dPo2fPnqisrAQA5OTk4N5777VoWLJOcrkMcx6/D/OWfoOV6/dy73Ui\nIiIiMzGpWe/atStGjBiBKVOm6MdWr16NI0eOYN26dXjvvfeQnp6OTz75xGJBybp18XPF48O7Y+2m\nA+jfwwcP3hcgdSQiIiKiFs+kNeuFhYWIj483GJs4cSKUSiUEQcD06dNx6NAhiwSkluOx4d0R0skd\nOZ/9guq6C1LHISIiImrxTGrWPT09UVxcbDBWUlICDw8PAMDly5dhY2PSJD21YnK5DM9P7gudKOLt\ntbug1YlSRyIiIiJq0UzqsBcuXIg5c+agW7du8PX1hUqlwm+//Ybly5cDAH755Rf83//9n0WDUsug\n8HTCM3/vhaXrfsYnmw9g0qgQqSMRERERtVgmNeuDBw/G5s2bsXXrVlRXVyMiIgIRERFwd3fXHx88\neLBFg1LLMbRvIH757TT+vfkAund0R78ePlJHIiIiImqRTN5n3cPDAwMGDED//v0xYMAAfaNuLleu\nXEFaWhpGjRqF2NhYvPzyywCAY8eOIS4uDlFRUYiLi0NFRYVZr0vmJwgCnp3QG118XfHWmp+grqmX\nOhIRERFRi2RSs15dXY34+HiMHDkSs2bNwsiRIzF58mRUVVWZLciSJUvg4OCAL7/8Ehs3bsTcuXMB\nAKmpqYiPj0dRUREmTZqElJQUs12TLMfeVo4Xp/WHCOC1j3/ApctXpY5ERERE1OKY1KynpaUhJCQE\npaWl2L59O0pLS9GjRw+kpqaaJcSFCxewYcMGzJkzRz/m4eGB2tpalJeXIzo6GgAQExODsrIy1NXV\nmeW6ZFkKTyfMn9wXx1Rn8dban3jDKREREdEdMmnN+k8//YTly5fD1tYWAODo6IgXXngBQ4YMMUuI\niooKuLm5ISsrCzt37oSTkxPmzJkDBwcH+Pj4QBAEAIBMJoO3tzfUavVNy3A0Gg00Go3BmFwuh6+v\nr1kyUtP06+GDp8b2xPvrf8XHhfvwVGxPqSMRERERWYxKpYJWqzUYc3FxgYuLS5POZ1Kz7urqisOH\nDyMk5K+dPY4cOdLki95Iq9Xi+PHj6NmzJ1544QXs2bMHzzzzDJYvXw5RNG02Ni8vD9nZ2QZj/v7+\nKC4uRnJyMmpqasySlZrGyS4U678Bvv5yA5yuWsd9BwkJCVJHICvEuiBjWBdkDOuCrufp6YmMjAxM\nnjwZlZWVBscSExMxa9asJp3XpGZ9+vTpmDZtGiZMmAA/Pz+cPHkSBQUFBstW7oafnx9sbGwwevRo\nAECvXr3g4eEBe3t7VFdXQxRFCIIAnU6H6upqKBSKm84xdepUjB8/3mBMLpcDADIyMsySk5pOq9Xh\n1Y9L8WM5MH3SVDwUJu0nnCYkJCA3N1fSDGR9WBdkDOuCjGFdUGPWrFljdGa9qUxq1h977DEEBgai\nsLAQBw4cgLe3N9566y0MGjSoyRe+nru7O8LDw7Fjxw488MADOHr0KGpqahAUFISQkBAolUrExsZC\nqVQiNDTU6E40d/P2AlmeXC7Dgin98cr732Ppul1wsJNjYE8uUSIiIqLWxdxLsE3+2NFBgwYZNOda\nrRbLly832+x6WloakpOT8frrr8PW1hZvvPEG2rdvj7S0NCQlJSEnJweurq7IzMw0y/Wo+dnbyrHw\nyQFIyf0Wmf/vR6ROD0ef7t5SxyIiIiKyWiY36zfSarVYsWKF2Zr1wMBA/Otf/7ppPCgoCPn5+Wa5\nBknP0cEWaU8PQnLODiz+sBQLnxiA++5hw05ERERkjMkfimSMqTd/El3P2dEOixPuh38HJyz6YCe+\n23tS6khEREREVumumvU/t1QkulNuzvbImPkAggNc8fr/+xHFP1rHDjFERERE1uSWy2C+++67Ro81\nNDSYPQy1Le3/mGF/9aOdWLruZ5w5dxnjH+rKHwKJiIiI/nDLZv2ll1665Yv5gUN0t9rZ2+DlpwZi\n6bpd+KiwDCeqz2PmI71ha3NXb/oQERERtQq3bNaLi4ubKwe1YXa2cvwzvh8CvA/g35sPQFVTjxen\nDoCLk53U0YiIiIgkxelLsgoymYDJUSF4fnJfHPi9DvOWluDA77VSxyIiIiKSFJt1sioPhQXg9X8M\nBgQBC7K34z8lh7jrEBEREbVZbNbJ6nTv6I7l8yIw4G8KfKjch0Uf7ESd5pLUsYiIiIiaHZt1skrt\nHe3w4tT+mDHuXvzy2yk8u6QYxT8e5yw7ERERtSls1slqCYKAMUOC8M7zDyHQxxlL1+3Cog92orr2\ngtTRiIiIiJoFm3WyegHeznjtH4Px9Lie2Hv4NGZmbsHqonJcunxV6mhEREREFnXLrRuJrIVcJiB2\nSDAG9vRF3hdl+GTzQWzeWYH/e7gHhvYNgFzOnzuJiIio9WGHQy2Kt7sj/hnfD0sSh8DD1QHLP/kZ\nM5cUo/jHCmi1OqnjEREREZkVm3VqkXp08cDbcx5E8rQBaGdng6XrfsbMzGIotx3BhUsNUscjIiIi\nMgsug6EWSxAEDLrXFwN7KrBznxqfbfkNK9fvxb/+V44RAzpi1MBO6KhwkTomERERUZOxWacWTxAE\nDOzpi4E9fXHg91oUbj+K/357FBu3HUFwgCuG9g3Eg/f5w93ZQeqoRERERHfEapr1yMhIODg4wM7O\nDoIgYP78+XjggQdw7NgxJCUl4cyZM3Bzc8OSJUvQsWNHqeOSlbqnkwfu6eSBJ2P/hm0/V6L4p+NY\nteFXfKjch55BnugfqsCAUB+pYxIRERGZxGqadUEQkJWVheDgYIPx1NRUxMfHIyYmBhs3bkRKSgry\n8vIkSkkthbuzA2IfDEbsg8GoUGtQsusEdu5T44ONv+KDjb/CxvFB5BbsQc9gL4QGeXDWnYiIiKyS\n1TTroije9OmUtbW1KC8vR3R0NAAgJiYGixcvRl1dHdzd3aWISS1QR4ULpowOxZTRoVDX1OPH8ip8\n/GkxvvqhAoU7jgIA/Du0R/eObggOcEOQvyuC/Fzh1M5W4uRERETU1llNsw4A8+fPhyiK6Nu3L+bN\nmweVSgUfHx8IggAAkMlk8Pb2hlqtvqlZ12g00Gg0BmNyuRy+vr7Nlp+sn8LTCTGDg6D8Vybeffs9\nHD5xBvuO1ODXIzXYffAUvv7pxHXPdYR/h/bw9XKCn1d7+HW49ruXWzvY2nAjJSIiIrqZSqWCVqs1\nGHNxcYGLS9M2vRDEG6ezJVJVVQUfHx80NDTg1VdfRX19PaZNm4YFCxagsLBQ/7zo6Gi8+eab6NGj\nh8Hrs7KykJ2dbTDm7++P4uJiJCcno6amplm+D2rZtIIdGmSuaJC5oEHmDK3MCVdlThAFw59rZbrL\nkImXIRcvQS5ehky8BJl4BTKxQf9LEBsgwx+PYRX/zIiIiMhCPD09kZGRgcjISFRWVhocS0xMxKxZ\ns5p0Xqtp1q938OBBPPvss8jPz8eoUaNQWloKQRCg0+kQHh6OTZs2cWad7kpCQgJyc3NNeq4oijhz\n7jJOnq7HyVPncfrsJdRqLqH27CXUai6iVnMJZ85dhu4W/5LkMgEOdnLY28lhb2vzx+/XvrazvfZY\nLhdgI5dBLhMgl8tg8+fv8mu/XxsXYCOTQS4XIAgCBAEQIEAmAIJMgAD8NS789bVMBuCP50H44/k3\nPe/ac64nGH55w1Ho3/W61ZNMes1Nz7nxHLc+qbEz3uk5AGDp0qWYN2/ebfNR29LW68KEf7Jt0ttv\nv43nnntO6hhkRTopXODa3t7sM+tWsQzm4sWL0Gq1aN++PQDgiy++QGhoKDw8PNCjRw8olUrExsZC\nqVQiNDTU6Hr1u/lDILoVQRDg7uIAdxcH/C3I0+hztFodzl9suPbrwpU/fv/j64tXcPmK9tqvBsPf\nL125ivpLDbjSoMVVrQitVgetToRWK+KqVgetTqcfv9UPA2Qm7cKxcMW3Uqcga8O6IGPaDcRL77Eu\n6C+De/thwZT+Zp8otopm/fTp05g9ezZ0Oh10Oh2Cg4Px8ssvAwDS0tKQlJSEnJwcuLq6IjMzU+K0\nRDeTy2VwbW8P1/b2FruGTif+0cjrcFUnAqII8Y9xANCJIkTxz5u18ddjXPtdJ4qAaOR5+Ovx9W58\n0+2mnxWM/PAg3jB4u/ftjL2xd7vr3JTTSJCmXBcA3nzzTcyfP//WL6Y2py3XBecIGvfWm2/h+fnP\nSx2DrEhHH2eLnNcqmvXAwED85z//MXosKCgI+fn5zZyIyPrIZAJkMoE3t1qQva4OPYO9pI5BVoZ1\nQcbY62pxL+uCmgH/r09EREREZKXYrBMRERERWSk260REREREVorNOhERERGRlWKzTkRERERkpdis\nExERERFZKTbrRERERERWis06EREREZGVYrNORERERGSl2KwTEREREVkpNutERERERFaKzToRERER\nkZVis05EREREZKXYrBMRERERWSk260REREREVsrqmvXs7GyEhITg0KFDAIBjx44hLi4OUVFRiIuL\nQ0VFhcQJiYiIiIiah1U162VlZfjll1/g5+enH0tNTUV8fDyKioowadIkpKSkSJiQiIiIiKj5WE2z\nfuXKFSxatAhpaWn6sdraWpSXlyM6OhoAEBMTg7KyMtTV1UmUkoiIiIio+VhNs/7OO+9g7Nix8Pf3\n14+pVCr4+PhAEAQAgEwmg7e3N9RqtVQxiYiIiIiajY3UAQBg9+7d2Lt3L+bPn9/kc2g0Gmg0GoMx\nuVwOX1/fu41HrZCnp6fUEcgKsS7IGNYFGcO6oMaoVCpotVqDMRcXF7i4uDTpfIIoiqI5gt2NlStX\nYvXq1bC1tYUoiqiqqoKXlxeSkpKQmpqKnTt3QhAE6HQ6hIeHY9OmTXB3dzc4R1ZWFrKzsw3GwsLC\nsG7duub8VoiIiIioDZs4cSJ27dplMJaYmIhZs2Y16XxW0azfKDIyEu+//z6Cg4MxZcoUTJgwAbGx\nsdiwYQMKCgqQl5d302uMzayr1Wq89dZbePvttznDTnoqlQqTJ0/GmjVrWBekx7ogY1gXZAzrgoxR\nqVR47rnn8Pzzz0OhUBgcu5uZdatYBnMjQRDw588QaWlpSEpKQk5ODlxdXZGZmWn0NY39Iezateum\ntyKobdNqtaisrGRdkAHWBRnDuiBjWBdkjFarxa5du6BQKBAQEGC281pls75lyxb946CgIOTn50uY\nhoiIiIhIGlazGwwRERERERlis05EREREZKXkadd/ClErZG9vj/DwcNjb20sdhawI64KMYV2QMawL\nMoZ1QcZYoi6scjcYIiIiIiLiMhgiIiIiIqvFZp2IiIiIyEq12mb92LFjiIuLQ1RUFOLi4lBRUSF1\nJGoGZ86cwYwZM/Dwww9j7NixmD17Nurq6gDcuiZYL21HdnY2QkJCcOjQIQCsi7buypUrSEtLw6hR\noxAbG4uXX34ZAOuirfv6668xfvx4jBs3DmPHjsXmzZsBsC7amszMTAwbNszg/xlA0+ugyTUitlJT\npkwRlUqlKIqiuGHDBnHKlCkSJ6LmcObMGbG0tFT/dWZmpvjSSy+JonjrmmC9tA379u0Tp0+fLg4d\nOlT87bffRFFkXbR1ixcvFl977TX91zU1NaIosi7auv79+4uHDh0SRVEU9+/fL953332iKLIu2pqf\nfvpJVKvVYmRkpP7/GaLY9Dpoao20yma9pqZG7N+/v6jT6URRFEWtViv269dPrK2tlTgZNbcvv/xS\nfOKJJ25ZE6yXtuHy5cvi448/Lp44cULfrLMu2rb6+nqxX79+4oULFwzGWRcUHh4u7tq1SxRFUSwt\nLRVHjRol1tTUiP369WNdtEHXT/A09b8Pd1MjVvkJpndLpVLBx8cHgiAAAGQyGby9vaFWq+Hu7i5x\nOmouoihi3bp1GD58+C1rQqfTsV7agHfeeQdjx46Fv7+/fox10bZVVFTAzc0NWVlZ2LlzJ5ycnDBn\nzhw4ODiwLtq4pUuXYubMmXB0dER9fT1WrlwJlUoFhULBumjjmvr/jbupkVa7Zp1o0aJFcHJywuTJ\nk6WOQhLbvXs39u7di4kTJ0odhayIVqvF8ePH0bNnT3z++eeYP38+Zs2ahQsXLkDkrsZtllarxcqV\nK7FixQoUFxfjvffew9y5c3HhwgWpo1Eb1Spn1n19fVFVVQVRFCEIAnQ6Haqrq6FQKKSORs0kMzMT\nFRUVyM3NBXDrmhBFkfXSypWWluLo0aMYNmyY/u/7qaeeQlJSEuuiDfPz84ONjQ1Gjx4NAOjVqxc8\nPDxgb2+P6upq1kUbVV5ejlOnTqFPnz4AgLCwMLRr1w729vb87wU1uZ+4mxpplTPrHh4eCAkJgVKp\nBAAolUqEhobyrag2YunSpSgrK0NOTg5sbK79PHqrmmC9tH4zZszA1q1bsWXLFhQXF8PHxwcffvgh\nHn74YdZFG+bu7o7w8HDs2LEDAHD06FHU1NQgKCiIddGGKRQKqNVqHD16FABw+PBh1NTUoHPnzqyL\nNuzPd9ua2k/cTY202k8wPXLkCJKSkqDRaODq6orMzEx07txZ6lhkYYcOHcKYMWPQuXNn/Uf9BgYG\nIisr65Y1wXppW4YNG4bc3Fx07dqVddHGHT9+HMnJyThz5gxsbW3x3HPPYfDgwayLNq6wsBC5ubmQ\ny+UAgNmzZyMyMpJ10cakp6dj8+bNqKmpgZubG9zd3aFUKptcB02tkVbbrBMRERERtXStchkMERER\nEVFrwGadiIiIiMhKsVknIiIiIrJSbNaJiIiIiKwUm3UiIiIiIivFZp2IiIiIyEqxWSciskI6nQ73\n3Xcf1Gq1WZ97p3JycpCWlmb2896Jp556CoWFhZJmICKSCvdZJyIyg/vuuw+CIAAALl68CDs7O8hk\nMgiCgEWLFiEmJkbihHevoqICI0eOxP79+y12jWXLlqGqqgqvvfaaxa5BRNSS2EgdgIioNfj555/1\nj4cNG4ZXX30VAwcObPT5Wq1W/+mILYUoivofSJqiJX7PRERS4zIYIiIzE0URN75puWzZMsybNw/P\nP/88+vbtC6VSid27d+Pxxx9H//79MWTIEKSnp0Or1QK41tiGhITg5MmTAIB//vOfSE9Px9NPP42w\nsDDExcWhsrLyjp8LAN988w1GjRqF/v37Iz09HRMnTsT69euNfi/Lli3Diy++CACIj48HcO1dhLCw\nMPz6668AgE8//RQPP/wwwsPDMWPGDP1ynD9zrV27FiNHjsTo0aMBAIsXL0ZERAT69euHRx99VP+D\nTklJCVatWgWlUon77rsPjzzyCABg0qRJ+nyiKCI7OxuRkZF44IEH8OKLL6K+vh7AtZn/kJAQrF+/\nHhEREbj//vuxcuXKpv0lEhFZCTbrRETN5KuvvkJsbCx++uknjB49GjY2NnjppZdQWlqKdevWYfv2\n7fj3v/+tf/6Ns9hffPEF5s2bhx9++AG+vr5Yvnz5HT+3pqYG8+bNQ1JSEr7//nsEBARg7969JuVf\ns2YNgGvvIuzatQs9e/ZEUVERPvzwQ6xYsQLfffcdevXqheeff97gdV9//TU+//xzKJVKAEDv3r1R\nWFiI0tJSjBo1CnPmzEFDQwMeeughTJ8+HWPGjMHPP/+Mzz///KYM+fn5KCwsxOrVq7F582acPXsW\n6enpBs/ZvXs3vvrqK6xatQpZWVmoqKgw6fsjIrJGbNaJiJpJ3759ERERAQCws7NDz5490atXLwiC\ngICAADz22GP44Ycf9M+/cXZ+1KhRCA0NhVwux5gxY1BeXn7Hzy0pKUFoaCiGDh0KuVyOadOmwc3N\nrcnfU35+PhISEtCpUyfIZDI888wz2LNnD6qrq/XPeeaZZ+Ds7Aw7OzsAQGxsLJydnSGTyfDUU0/h\n/PnzJjfUhYWFeOqpp+Dn5wdHR0c899xzBjefCoKA2bNnw9bWFqGhoejWrZtF19gTEVka16wTETUT\nX19fg6+PHDmCzMxM7Nu3DxcvXoROp0OvXr0afb2Xl5f+cbt27XDhwoU7fm51dTUUCoXBc2/8+k5U\nVlZi0aJFyMjIAHDthwYbGxuo1Wp4enoaPf/777+PgoICnD59GgBw6dIl1NXVmXS96upq+Pn56b/2\n8/NDQ0MDamtr9WMeHh76xw4ODrf8cyIisnZs1omIJJKamoo+ffpg+fLlcHBwwIcffoiSkhKLXrND\nhw7YsWOHwVhVVZVJrzV2c6mfnx/mzp2Lhx9++KZjf66/v/51O3fuRF5eHvLy8hAcHAzg2jsOf74z\ncLsbWL29vfVr8wHg5MmTsLOzg4eHB86fP2/S90FE1JJwGQwRkUTq6+vh7OwMBwcHHD58GJ988onF\nrzl06FCUlZWhpKQEWq0WH3/8scmz2h4eHhAEAcePH9ePPf7443jvvfdw+PBhAIBGo8GXX37Z6Dnq\n6+thY2MDNzc3XLlyBe+88w4uXbqkP+7l5WVwM+yNoqOj8dFHH6GyshLnz5/HsmXLDLbF5G7ERNTa\nsFknIjIzU7c3XLBgAQoKChAWFoa0tDT9binGznO7c5r6XE9PTyxduhSvvfYaBg4ciBMnTiA0NFS/\nnlSq+OoAAAETSURBVPxWnJycMGPGDDz22GMYMGAA9u3bh6ioKDz55JOYO3cu+vXrh3HjxhnM3N+Y\nJSIiAoMGDcLIkSMxfPjw/9/e3aNICARhAK3ACTXzCJ5AMDMVxgOYzDWMPIagFzKe20wkMmy2wf4l\nG9jge2lDd4UfTVV3FEURZVl+rt/v99j3PZqmiWEYvu0xDEP0fR+PxyO6ros8z2Oapl/P+89TkwAp\n8CkSwIW93+9o2zbmeY66rs8uB4Av3KwDXMy2bfF6vWLf91iWJbIs+3OwFYDzGDAFuJjn8xnjOMZx\nHFFVVazrGrfb7eyyAPiBNhgAAEiUNhgAAEiUsA4AAIkS1gEAIFHCOgAAJEpYBwCARAnrAACQqA9O\nEu69wNm6EQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x16527000bc10\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the loss evolution\n",
        "plt.figure(figsize=(12, 4))\n",
        "plt.plot(lls_)\n",
        "plt.xlabel(\"Training iteration\")\n",
        "plt.ylabel(\"Log marginal likelihood\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "1DOkwqQEsXVs"
      },
      "outputs": [],
      "source": [
        "# Having trained the model, we'd like to sample from the posterior conditioned\n",
        "# on observations. We'd like the samples to be at points other than the training\n",
        "# inputs.\n",
        "predictive_index_points_ = np.linspace(-1.2, 1.2, 200, dtype=np.float64)\n",
        "# Reshape to [200, 1] -- 1 is the dimensionality of the feature space.\n",
        "predictive_index_points_ = predictive_index_points_[..., np.newaxis]\n",
        "\n",
        "optimized_kernel = tfk.ExponentiatedQuadratic(amplitude_var, length_scale_var)\n",
        "gprm = tfd.GaussianProcessRegressionModel(\n",
        "    kernel=optimized_kernel,\n",
        "    index_points=predictive_index_points_,\n",
        "    observation_index_points=observation_index_points_,\n",
        "    observations=observations_,\n",
        "    observation_noise_variance=observation_noise_variance_var,\n",
        "    predictive_noise_variance=0.)\n",
        "\n",
        "# Create op to draw  50 independent samples, each of which is a *joint* draw\n",
        "# from the posterior at the predictive_index_points_. Since we have 200 input\n",
        "# locations as defined above, this posterior distribution over corresponding\n",
        "# function values is a 200-dimensional multivariate Gaussian distribution!\n",
        "num_samples = 50\n",
        "samples = gprm.sample(num_samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 322
        },
        "colab_type": "code",
        "id": "1XgqrfsSub15",
        "outputId": "3aa481c5-ef3c-45cf-a104-baf89f74fa47"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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FL+5wfGMuAL/hhht45plnWL58OZa1/eGdf/75zJs3b5vbtizBLFq06C0f4/5GKUWQz+MP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\nrkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x165271e1f810\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the true function, observations, and posterior samples.\n",
        "plt.figure(figsize=(12, 4))\n",
        "plt.plot(predictive_index_points_, sinusoid(predictive_index_points_),\n",
        "         label='True fn')\n",
        "plt.scatter(observation_index_points_[:, 0], observations_,\n",
        "            label='Observations')\n",
        "for i in range(num_samples):\n",
        "  plt.plot(predictive_index_points_, samples[i, :], c='r', alpha=.1,\n",
        "           label='Posterior Sample' if i == 0 else None)\n",
        "leg = plt.legend(loc='upper right')\n",
        "for lh in leg.legendHandles: \n",
        "    lh.set_alpha(1)\n",
        "plt.xlabel(r\"Index points ($\\mathbb{R}^1$)\")\n",
        "plt.ylabel(\"Observation space\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "aZe4H-7jy0hR"
      },
      "source": [
        "*Note: if you run the above code several times, sometimes it looks great and\n",
        "other times it looks terrible! The maximum likelihood training of the parameters\n",
        "is quite sensitive and sometimes converges to poor models. The best approach\n",
        "is to use MCMC to marginalize the model hyperparameters.*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "NThOGRM1oxuW"
      },
      "source": [
        "## Marginalizing hyperparameters with HMC"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "RdCdMag7ymYp"
      },
      "source": [
        "Instead of optimizing the hyperparameters, let's try integrating them out with Hamiltonian Monte Carlo. We'll first define and run a sampler to approximately draw from the posterior distribution over kernel hyperparameters, given the observations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "t1sZUooao1D0"
      },
      "outputs": [],
      "source": [
        "num_results = 100\n",
        "num_burnin_steps = 50\n",
        "\n",
        "sampler = tfp.mcmc.TransformedTransitionKernel(\n",
        "    tfp.mcmc.HamiltonianMonteCarlo(\n",
        "        target_log_prob_fn=target_log_prob,\n",
        "        step_size=tf.cast(0.1, tf.float64),\n",
        "        num_leapfrog_steps=8),\n",
        "    bijector=[constrain_positive, constrain_positive, constrain_positive])\n",
        "\n",
        "adaptive_sampler = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
        "    inner_kernel=sampler,\n",
        "    num_adaptation_steps=int(0.8 * num_burnin_steps),\n",
        "    target_accept_prob=tf.cast(0.75, tf.float64))\n",
        "\n",
        "initial_state = [tf.cast(x, tf.float64) for x in [1., 1., 1.]]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 34
        },
        "colab_type": "code",
        "id": "MyOYZ0LEpnjQ",
        "outputId": "c172f9c9-2cd9-4cf8-84ea-fc0e9ae18aec"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Inference ran in 48.94s.\n"
          ]
        }
      ],
      "source": [
        "# Speed up sampling by tracing with `tf.function`.\n",
        "@tf.function(autograph=False, experimental_compile=False)\n",
        "def do_sampling():\n",
        "  return tfp.mcmc.sample_chain(\n",
        "      kernel=adaptive_sampler,\n",
        "      current_state=initial_state,\n",
        "      num_results=num_results,\n",
        "      num_burnin_steps=num_burnin_steps,\n",
        "      trace_fn=lambda current_state, kernel_results: kernel_results)\n",
        "\n",
        "t0 = time.time()\n",
        "samples, kernel_results = do_sampling()\n",
        "t1 = time.time()\n",
        "print(\"Inference ran in {:.2f}s.\".format(t1-t0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "zAySwdGWy8Jm"
      },
      "source": [
        "Let's sanity-check the sampler by examining the hyperparameter traces. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 223
        },
        "colab_type": "code",
        "id": "_5GA7jzwwPT9",
        "outputId": "a05d1846-8ab2-4506-a114-8d6282e8958f"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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pQwnZVoAW7zUAgMrwBwg7zkPYOR52tQsVkW1o8t0IAHDLTfBIZ9DhmQ4AKI9+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\ncQSxRwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x1652745d2250\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "(amplitude_samples,\n",
        " length_scale_samples,\n",
        " observation_noise_variance_samples) = samples\n",
        "\n",
        "f = plt.figure(figsize=[15, 3])\n",
        "for i, s in enumerate(samples):\n",
        "  ax = f.add_subplot(1, len(samples) + 1, i + 1)\n",
        "  ax.plot(s)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "BQoBYHsAzJr3"
      },
      "source": [
        "Now instead of constructing a single GP with the optimized hyperparameters, we construct the *posterior predictive distribution* as a mixture of GPs, each defined by a sample from the posterior distribution over hyperparameters. This approximately integrates over the posterior parameters via Monte Carlo sampling to compute the marginal predictive distribution at unobserved locations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "XzZmJc7yrNGJ"
      },
      "outputs": [],
      "source": [
        "# The sampled hyperparams have a leading batch dimension, `[num_results, ...]`,\n",
        "# so they construct a *batch* of kernels.\n",
        "batch_of_posterior_kernels = tfk.ExponentiatedQuadratic(\n",
        "    amplitude_samples, length_scale_samples)\n",
        "\n",
        "# The batch of kernels creates a batch of GP predictive models, one for each\n",
        "# posterior sample.\n",
        "batch_gprm = tfd.GaussianProcessRegressionModel(\n",
        "    kernel=batch_of_posterior_kernels,\n",
        "    index_points=predictive_index_points_,\n",
        "    observation_index_points=observation_index_points_,\n",
        "    observations=observations_,\n",
        "    observation_noise_variance=observation_noise_variance_samples,\n",
        "    predictive_noise_variance=0.)\n",
        "\n",
        "# To construct the marginal predictive distribution, we average with uniform\n",
        "# weight over the posterior samples.\n",
        "predictive_gprm = tfd.MixtureSameFamily(\n",
        "    mixture_distribution=tfd.Categorical(logits=tf.zeros([num_results])),\n",
        "    components_distribution=batch_gprm)\n",
        "\n",
        "num_samples = 50\n",
        "samples = predictive_gprm.sample(num_samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 317
        },
        "colab_type": "code",
        "id": "QwfcWtDfyayd",
        "outputId": "f6890099-10cc-487a-9111-33a975dc3c44"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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Z6JlK2hjGNQ/lOGiGMdFPXwghhBBiUhtzAP7ggw/yxz/+kcHBQV5etfLNb35z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\n4C/ROHQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x3b0b5bc4590\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the true function, observations, and posterior samples.\n",
        "plt.figure(figsize=(12, 4))\n",
        "plt.plot(predictive_index_points_, sinusoid(predictive_index_points_),\n",
        "         label='True fn')\n",
        "plt.scatter(observation_index_points_[:, 0], observations_,\n",
        "            label='Observations')\n",
        "for i in range(num_samples):\n",
        "  plt.plot(predictive_index_points_, samples[i, :], c='r', alpha=.1,\n",
        "           label='Posterior Sample' if i == 0 else None)\n",
        "leg = plt.legend(loc='upper right')\n",
        "for lh in leg.legendHandles: \n",
        "    lh.set_alpha(1)\n",
        "plt.xlabel(r\"Index points ($\\mathbb{R}^1$)\")\n",
        "plt.ylabel(\"Observation space\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "bzCP7uFlzpq5"
      },
      "source": [
        "Although the differences are subtle in this case, in general, we would expect the posterior predictive distribution to generalize better (give higher likelihood to held-out data) than just using the most likely parameters as we did above."
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Gaussian Process Regression In TFP",
      "private_outputs": false,
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
